Purchase Solution

Proof in Group Theory

Not what you're looking for?

Ask Custom Question

Let C* be the multiplicative group of nonzero complex numbers and R** be the multiplicative group of positive real numbers. Prove that C* is isomorphic to R** X R/Z where R is the additive group of real numbers.

Purchase this Solution
Solution Summary

We prove that the multiplicative group of nonzero complex numbers is isomorphic to the direct product of the multiplicative group of positive real numbers and the additive group of real number modulo the integers.

Solution Preview

We wish to show that where is the additive group of real numbers, is the multiplicative group of positive real numbers, and is the multiplicative group of nonzero complex numbers.
Consider ...

Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

View More Free Quizzes
Related BrainMass Solutions

  • Group Theory proof

    91056 Group Theory Proof See the attached file.

  • Group theory

    237862 Group Theory Proof: Pigeonhole Principle and Inverse Elements Please help with the following problems involving group theory proofs. Provide step by step calculations along with explanations.

  • Counting Principle: Permutation Groups

    see attached This is a group theory proof regarding permutations and counting.

  • Group Theory - Group of Even Order

    57927 Group Theory - Group of Even Order Modern Algebra Group Theory (XXII) Group of Even Order If G is a group of even order, prove it has an element a which is not equal to e satisfying a^2 = e.

  • Description of Abelian group

    56966 Description of Abelian group Modern Algebra Group Theory (VII) To prove that if G is an abelian group, then

  • Graph theory

    This is a proof regarding odd numbers of people in a group.

  • group theory

    By the same reason in (a), we must have . Therefore, . This solution uses the following two Lemmas which are simple facts for group theory.

  • Show that the group G is abelian if (ab)^2=a^2b^2

    This shows how to complete a proof regarding an Abelian group. The solution is detailed and well presented.

  • Problems in Group Theory

    463173 Problems in Group Theory See the attached file. Suppose that G is a finite group and H is a normal subgroup of G. (i) Explain briefly how the quotient group G/H is defined.

  • Group Theory Proof Form

    212645 Group Theory Let G be a finite group with K is a normal subgroup of G. If (l K l, [G:K]) =1, prove that K is unique subgroup of G having order l K l.

View More Related Solutions